Real world data does not always lay on a low-dimensional linear manifold, but can instead be most naturally represented by low-dimensional non-linear manifold. There is a large extent literature on such methods, which is beyond the scope of the current text. However, the interested reader can look to [1]}, and references therein, for details on such methods. However, we compare our AE based technique with an important method in this domain called Isomap [2]}. In particular, we will compare the non-linear DE capabilities of Isomap with our proposed autoencoder based algorithm, so in this section we provide a brief overview of Isomap and more in-depth derivation of autoencoders.
